Conventional articles of athletic footwear often include an upper and a sole structure. The upper provides a covering for the foot that securely receives and positions the foot with respect to the sole structure. The sole structure is typically secured to a lower surface of the upper and positioned between the foot and the ground (or other contact surface) during wear of a shoe incorporating that upper and sole structure. The sole structure may include a midsole and an outsole. The midsole may help control foot motion and attenuate impact forces. For example, various midsoles may include elements formed from a foam material and/or include a fluid-filled bladder to help cushion a wearer foot. Although such elements provide many advantages, they may lack other qualities that may be desirable. For example, many conventional impact attenuation members lack “springiness,” i.e., they lack a feel of bounce or recoil that can be beneficial in some activities. There remains a need for sole structures that include impact attenuation elements while also having other desirable properties.